Multi-level Data Fusion Strategies for Modeling Three-way Electrophoresis Capillary and Fluorescence Arrays Enhancing Geographical and Grape Variety Classification of Wines

0 Multi-level Data Fusion Strategies for Modeling Three-way 1 Electrophoresis Capillary and Fluorescence Arrays 2 Enhancing Geographical and Grape variety Classification of 3 Wines 4 Rocío Ríos-Reina a , Silvana M. Azcarate b ,* , José M. Camiña b , Héctor C. Goicoechea c 5 Affiliations 6 a Área de Nutrición y Bromatología, Fac. Farmacia, Univ. Sevilla, C/P. García González 7 no. 2, E-41012 Sevilla, Spain. 8 b Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La Pampa- 9 CONICET, and Instituto de Ciencias de la Tierra y Ambientales de La Pampa 10 (INCITAP), Av. Uruguay 151 (6300) Santa Rosa, La Pampa, Argentina. 11 c Laboratorio de Desarrollo Analítico y Quimiometría (LADAQ), Cátedra de Química 12 Analítica I, Facultad de Bioquímica y Ciencias Biológicas, Universidad Nacional del 13 Litoral-CONICET, Ciudad Universitaria, Santa Fe (S3000ZAA), Argentina 14 * To whom correspondence should be addressed. E-mail [email protected] 15 16 17 1 18 Abstract 19 Capillary electrophoresis with diode array detection (CE-DAD) and multidimensional 20 fluorescence spectroscopy (EEM) second-order data were fused and chemometrically 21 processed for geographical and grape variety classification of wines. Multi-levels data 22 fusion strategies on three-way data were evaluated and compared revealing their 23 advantages/disadvantages in the classification context. Straightforward approaches 24 based on a series of data preprocessing and feature extraction steps were developed for 25 each studied level. Partial least square discriminant analysis (PLS-DA) and its multi- 26 way extension (NPLS-DA) were applied to CE-DAD, EEM and fused data matrices 27 structured as two-way and three-way arrays, respectively. Classification results 28 achieved on each model were evaluated through global indices such as average 29 sensitivity non-error rate and average precision. Different degrees of improvement were 30 observed comparing the fused matrix results with those obtained using a single one, 31 clear benefits have been demonstrated when level of data fusion increases, achieving 32 with the high-level strategy the best classification results. 33 34 Keywords: Electrophoresis capillary, Multidimensional Fluorescence Spectroscopy, 35 Three-way data modeling, Multi-level data fusion, Classification. 36 37 38 39 2 40 1. Introduction 41 In multivariate classification setting, second-order data handling is producing a 42 significant impact on the development of analytical strategies, especially for 43 determining characteristic patterns of the analytes of interest in highly complex matrices 44 [1, 2]. In particular, food characterization tasks are in an innovative progressive change 45 going from the development of dedicated methods for quantification of specific 46 compounds to the fingerprint acquisition by rapid, non-destructive and non-selective 47 instrumental techniques [3–5]. 48 Hence, second-order data, especially three-way arrays modeling applications, 49 could supply interesting improvements as regards results attained when extremely 50 complex systems should be classified. Thereby, it has been demonstrated that data 51 analysis can be more effective when modeling second- or higher -data with multiway 52 algorithms compared to unfolding procedures [1, 6]. Otherwise, it has been recently 53 revealed that the ability in terms of discrimination power can be improved by using 54 second-order data arranged in a three-way structure instead of first-order data [2]. 55 Over the years, analytical methods and data analysis tools commonly used in 56 food quality and process control had to be re-evaluated and modified to fit these new 57 tasks [1]. In this progression of gathering more and better information, the multivariate 58 statistical analysis of fused data has become a powerful tool for enhancing the reliability 59 of the results. Being the key point how the information sources can be combined to 60 provide the joint classification prediction of the samples, three levels of data fusion 61 (DF) have been reported [7, 8]. 62 Firstly, low-level DF (1-DF) implies a simple concatenation of the individual 63 matrices to build a single array that is then used for calculating a single model for final 64 classification. In the food authentication and quality control field, it has been the most 65 3 used fusion approach to improve the results since is a common, conceptually simple, 66 first attempt with outputs from different sources providing first-order data [9–11]. 67 Nevertheless, out of the food analysis scope, three-way arrays have been concatenated 68 using low-level DF strategy in a recent original report [12]. 69 Secondly, mid-level DF (2-DF) first extracts some relevant features from each 70 data source separately and then these outputs are concatenated to build a single array to 71 be then processed by the desired chemometric technique. This approach has been 72 probably the one that has purposed more challenges chiefly for second-order data 73 analysis, where witty strategies for data compression, extraction or reduction have been 74 explored for improving outcomes. Mainly, the attempt has been addressed to evaluate 75 the combination of first- and second order data provided by multiple platforms since 76 data are very different in structure, size or scale [13–18]. Otherwise, the performance of 77 mid-level applications has commonly been compared to low-level fusion as well as to 78 single models [19–22]. 79 Lastly, the high-level DF (3-DF) builds separate models for the different blocks, 80 and the individual results are then integrated into a single final response. This strategy 81 has been lesser explored than the two mentioned above. Although several 82 methodologies for final identity declaration by modelling the individual matrices 83 independently have been reported [8, 23], only few of them have been inquired in food 84 classification context. High-level DF has been mainly implemented for the comparison 85 with the other two DF levels [24, 25]. 86 The aim of this work was to develop multiple strategies to assess the three DF 87 levels on two second-order arrays, with different data complexity, in order to know the 88 correlation and analogy between both information sources for twofold classification 89 purposes. The focus was put on the development of models able to distinguish among 90 4 white wines of three different grape varieties with geographical indication (GI) from the 91 four main wine production regions of Argentina [26]. For that, fluorescence excitation– 92 emission matrix spectroscopy (EEM), and capillary electrophoresis with diode array 93 detector (CE-DAD) were applied as non-target analysis in order to acquire a fingerprint 94 to characterize the wines. 95 To our best knowledge, it is the first time that the multi-levels of DF strategies 96 on second-order data are evaluated and compared revealing their 97 advantages/disadvantages in the classification context. Thus, we developed multiple and 98 straightforward approaches based on a series of data preprocessing and feature 99 extraction steps, which constitutes a significant improvement in the DF analysis, and it 100 offers a wide range of possibilities when second-order data of different nature are 101 assessed. Finally, the challenge consisted in finding the optimal combination of data 102 preprocessing, fused data and data modeling that would provide the best results. 103 104 2. Materials and methods 105 2.1. Samples 106 Thirty-nine samples of commercial white wine from four wine-producing 107 origins, all belonging to provinces of Argentina (Mendoza-M, San Juan-SJ, Salta-S, and 108 Rio Negro-RN) and three different grape varieties (Chardonnay-CH, Sauvignon Blanc- 109 SB and Torrontés-TO), were included in this study: 14 Chardonnay wines (10 from 110 Mendoza and 4 from San Juan), 13 Sauvignon Blanc wines (10 from Mendoza, 1 from 111 San Juan, and 2 from Río Negro) and 12 wines from grapes of the variety Torrontés (4 112 from Mendoza, 1 from San Juan, 5 from Salta, and 2 from Río Negro). Wine samples 113 were selected from the 2011 to 2013 vintages and bought from a local market. The 114 5 alcoholic content ranged from 12.2 to 13.8% v/v of ethanol. These samples were 115 analyzed in triplicate by the two techniques described below. 116 117 2.2. Data acquisition 118 2.2.1. EEM data 119 All spectrofluorimetric measures were acquired according to the method 120 reported by Azcarate et al. [26] using a Cary Eclipse Fluorescence Spectrophotometer 121 (Agilent Technologies, Waldbronn, Germany) with a 1×1 cm quartz fluorescence cell, 122 xenon flash lamp. CaryEcplise software package was used to control the instrument, 123 data acquisition and data analysis. Fluorescence excitation spectra were recorded by 124 varying the wavelengths between 245 and 341 nm (increment 5 nm), and by recording 125 the emission spectra from 300 to 500 nm (spaced by 0.5 nm interval). Fluorescence 126 measurements were done in triplicate for each sample. 127 128 2.2.2. CE-DAD data 129 The electrophoretic run conditions are treated in detail in our previous work [27] 130 and here only main analysis steps will be recalled. All electropherograms were acquired 131 on a CE system (Agilent Technologies, Waldbronn, Germany) equipped with a DAD 132 and an uncoated fused silica capillary of 40 cm total length (31.5 cm effective length) 133 and 75 µm inner diameter (MicroSolv Technology Corporation, Eatontown, NJ, USA). 134 Separation was performed by applying a voltage of 24 kV and with a typical current of 135 approximately 80 µA. The hydrodynamic injection was performed in the positive 136 electrode of the capillary by applying a pressure of 40 mbar for 8 s. The cartridge was 137 maintained at 25.0°C. The electropherograms were recorded during 10 min at 0.3 s 138 6 steps and recording UV spectra between 189 and 401 nm each 2 nm and samples were 139 analyzed by triplicate. 140 141 2.3. Data analysis 142 In order to extract and/or merge the information presented in each data set 143 obtained by the two different instrumental analysis of each sample, different 144 chemometric algorithms were employed. As both techniques produced out-puts with the 145 same data structure (i.e. three-way arrays), they were analyzed by similar algorithms in 146 order to decompose and compress the data. 147 The data analysis workflow developed in this study is schematized in Fig. 1. In 148 general terms, it includes: 1) building separate classification models on data obtained 149 from the individual analytical techniques by applying 3 different approaches; and 2) 150 building classification multiplatform models by applying different DF strategies: l-DF, 151 2-DF and 3-DF (assessing different approaches). Then, all the classification models 152 obtained were assessed and compared. 153 154 Insert here Fig. 1 155 156 2.3.1. Data set and preprocessing 157 In order to validate the classification models, the dataset corresponding to each 158 technique, containing 39 samples, was split into a training set of 24 samples (12 CH, 12 159 SB and 12 TO or 15 M, 4 SJ, 2 RN and 2 S) and a test set of 15 samples (6 CH, 5 SB 160 and 4 TO or 9 M, 2 SJ, 2 S, 2 RN) by using the Duplex algorithm [28], keeping the 161 triplicates in the same set (i.e. the training set contained 72 analysis and the test set 45 162 analysis). The split between training and test sets was done by keeping the ratio of 163 7 samples of each class like in the original set, balancing the representation of each 164 category and keeping the replicates together. Moreover, after checking by exploratory 165 analysis that both sets spanned the whole variability domain, the same split was 166 maintained for all the data sets (the individual and the fused data sets). 167 To find the optimal classification results for each class studied (variety or 168 origin), different preprocessing options were considered in each model: both mean 169 centering and autoscaling were used depending on the nature of the data, as well as none 170 preprocessing. 171 172 2.3.2. Decomposition and compression methods 173 As can be observed in Fig. 1, different decomposition and compression methods 174 (i.e. exploratory and reduction data analysis) were applied. Then, the features obtained 175 were used for the DF models. Thus, on the one hand, the original EEM and CE-DAD 176 three-way arrays (117×49×41 and 117×676×107, respectively, considering the samples 177 by triplicate) were unfolded in a multiset structure via row-wise augmentation and then 178 these new matrices (a matrix of 117×2009 for EEM unfolded data and of 117×72332 for 179 CE-DAD unfolded data), as well as the fusion of both, were used for the classification 180 or compressed by principal component analysis (PCA). 181 On the other hand, the EEM three-way array was decomposed by parallel factor 182 analysis (PARAFAC) [29] into trilinear components, related to the main fluorophores 183 present in the samples, whose scores (first mode loadings) were used as features for the 184 classification, or to build a fused dataset previous to the classification process. A three- 185 factor model, constrained with non-negativity in all modes, was obtained as the 186 optimum model according to the CORe CONsistency DIAgnostic test (COR-CONDIA) 187 [18, 30], the explained variance, the visual inspection of the profiles and residuals [26]. 188 8 Therefore, the three-way array matrix was decomposed by PARAFAC to three new 189 matrices containing the PARAFAC scores of the three fluorophores, as well as their 190 excitation and emission loadings. 191 Finally, CE-DAD array decomposition was carried out by Tucker3 and the 192 resulted A matrix (Tucker3 output with the concentrations) was directly used, or fused 193 in a new data set, for the classification purpose. In this study, Tucker3 was selected due 194 to the high complexity of the CE-DAD data, which require different number of factors 195 in each mode. The number of factors selected was 18, 18 and 6 for each recorder mode, 196 obtaining a model with a 95% of total explained variance. Non-negativity was imposed 197 as unique constraint in all modes in agreement with a previous work [27] and three 198 matrices A, B and C were obtained containing the concentration, electropherogram and 199 spectra profiles, respectively, together with a G core (18×18×6) corresponding to the 200 magnitude of the interaction among factors in different modes. 201 202 2.3.3. Classification methods 203 In this work, two classification techniques derived from the regression algorithm 204 partial least squares (PLS) were used: the PLS-DA (DA for discriminant analysis) [31] 205 for first-order data and its multi-way or multilinear extension (NPLS-DA) [32] for 206 second-order data (three-way arrays). In order to select the proper number of latent 207 variables (LVs), i.e. the dimensionality of the model, the minimum classification error 208 rate in cross-validation (venetian blind) was considered. In discriminant analysis, the 209 dependent variable, Y, holds the class information (as many y-variables as number of 210 classes). The raw predictions from a PLS-DA model is a value of nominally zero or one. 211 A value closer to zero indicates the new sample is not in the modeled class; a value of 212 one indicates a sample is in the modeled class [31]. 213 15 the visual assessment of all the fluorescence features of the grape varieties pointed out a 361 general trend for the spectral maxima to be shifted towards 450 and 350 nm of em/ex. 362 Furthermore, similar fluorescence trend was observed for the different origins but 363 maintaining the characteristic shape of its variety. 364 On the other hand, as can be seen in the CE-DAD landscapes (Fig. 2), they 365 showed many overlapping peaks corresponding to the complex mixture of chemical 366 compounds that are present in the white wines. Moreover, as was shown in a previous 367 report [27] a remarkable peak misalignment and shape deformation in electrophoretic 368 mode was produced. It could be also observed some differences between geographical 369 origins and grape varieties. Thus, all the samples showed marked peaks around 3 and 5 370 min but with strong differences among varieties and origins. From these observations, 371 all these differences could make possible the classification of the samples according to 372 origins and varieties. 373 374 Insert here Fig. 2 375 376 3.2. Individual models 377 3.2.1. General considerations 378 In the first stage, excitation-emission matrices (EEM) and capillary 379 electrophoresis (CE-DAD) data were treated separately to build the classification 380 models. The data matrices were organized and analyzed as two- and three-dimensional 381 arrays. Thus, three different classification approaches considering the data structures 382 and modeling were performed: (a) three-way data by PLS-DA using factors obtained 383 from a resolution method (PARAFAC or Tucker3); (b) three-way data by N-PLS-DA; 384 and (c) full unfolded data using PLS-DA (schematized in Fig. 1). 385 16 It should be noted that both datasets differ in the complexity of the data 386 structure. EEMs represents a well-known illustration of bilinear data fulfilling with the 387 so-called low rank trilinearity condition, which can be decomposed into the excitation 388 and the emission spectra for a given fluorescent component [2]. In return, the three- 389 dimensional array built from CE-DAD data is non-trilinear. Moreover, it presents 390 certain drawbacks like remarkable peak misalignment and shape deformation in a data 391 mode associated with deficiency rank in the other one. In those cases, in which multi- 392 way data are involved for classification issues, the choice of the appropriate multi-way 393 approach will be decisive in the validity of the solution found. 394 For building models, the latent variables were selected considering the lowest 395 CV classification error rate (data not shown). The best preprocess and region 396 (variables), together with the optimal configuration of each model, such as the number 397 of latent variables retained, were selected as those leading to the lowest inaccuracy and 398 highest sensitivity and specificity obtained with the prediction set. 399 400 3.2.2. Classification models for EEM data 401 For the approach (a) of Fig. 1, EEM dataset was arranged in a three-way data 402 array (72 training samples, 41 emission wavelengths and 49 excitation wavelengths) 403 and then, it was analyzed by means of PARAFAC. A three-factor model was chosen 404 representing the best compromise between explained variance (99.5%) and core 405 consistency (71%). The obtained model presented results that were in good agreement 406 with works presented in literature [26] where the loadings for second (emission) and, 407 third (excitation) modes and PCA scores have already been reported. 408 On the other hand, for the approach (c) of Fig 1, the EEM data array (72 × 49 × 409 41) was unfolded into a two-dimensional array (72 × 2009). To check the repeatability 410 17 of the measurements, detect outliers and recognize patterns in the samples’ distribution, 411 PCA analyses on PARAFAC factors and unfolded matrix were performed (Fig. IA. and 412 IB. SM). By analyzing the scores plots, it could not be observed a clear differentiation 413 of the samples by means of geographical origin on both two- and three-way data 414 structures, showing in both cases a similar overlapping, mainly between samples of M 415 and SJ. The same situation was observed when the differentiation among samples was 416 assessed by means of the three grape varieties, as it was shown in a previous report [26]. 417 A PLS-DA model was performed on the PARAFAC factors and the unfolded 418 matrix, which were prior preprocessed by autoscaling and mean centering, respectively. 419 On the other side, a classification model based on NPLS-DA on the three-way data 420 matrix was built (approach (b) of Fig 1). The obtained classification results of these data 421 sets are reported in Table 1 and Table 2, when grape variety and geographical origin 422 were used as classifier as well as in Fig. II and III. SM, respectively. Then separate 423 models were evaluated comparing the number of latent variables retained and the 424 indices derived from confusion matrix (Sens., Spec., Prec.; and PREC. and NER). 425 All the built models for sample classification according to grape variety showed 426 a similar performance that the obtained in a previous work [26]. However, in the present 427 study, the best individual model for grape variety classification seemed to be the NPLS- 428 DA model reaching the highest NER and PREC values in prediction stage being 81.1% 429 and 82.1%, respectively (Table 1). 430 Furthermore, suitable classification results were attained according to 431 geographical origin by the three built models. In this case, the model acquired from 432 PLSDA on the PARAFAC factors was the optimal reaching the highest rate of well- 433 classified samples in the prediction set and displaying the highest NER values (Table 434 2). 435 18 436 Insert here Table 1 437 Insert here Table 2 438 439 3.2.3. Classification models for CE-DAD data 440 For the (a) and (b) approaches (Fig 1), CE-DAD dataset was arranged in a cube 441 structure (72 training samples, 676 times and 107 wavelengths) and it was unfolded in a 442 matrix of size (72 × 72332) for the strategy (c). In order to avoid drawbacks, three-way 443 array was modeled by means of Tucker3 that allows using a different number of factors 444 in each mode. Thus, the number of eigenvalues explaining 95% of the variance of the 445 data were 18, 18 and 6, for modes 1, 2 and 3, respectively. After that, PCA analysis on 446 unfolded matrix and Tucker3 factors were performed. The scatter plots of these PCA 447 analyses are shown in Fig. IC. SM and Fig. ID SM, respectively. It can be seen that the 448 CE-DAD data showed higher variability than EEM data when the reproducibility was 449 assessed. 450 In the same way, PLS-DA was performed on the Tucker3 factors and the 451 unfolded matrix, applying autoscaling and mean centering as preprocessing, 452 respectively. On the other side, a classification model based on NPLS-DA on the three- 453 way data array was built (approach b). It is relevant to highlight that both (b) and (c) 454 approaches were able to deal rank deficiency [14]. 455 The three models for grape variety classification showed similar performances; 456 however, for prediction set, the NPLS-DA model attained higher indices of 66.1 and 457 70.8 for NER and PREC, respectively (Table 1). Concerning geographical origin 458 classification, despite the obtained models with the CE-DAD data achieved promising 459 results in the calibration stages, they were not able to predict the samples correctly. 460 19 Thus, they showed in all cases NER values lower than 56.9 % (Tabla 1). These 461 classification results could be also observed by looking the scores and loadings plots of 462 the PLS-DA models reported in Fig. II and III. SM. 463 Thus, the application of fusion approaches was expected to increase the overall 464 classification ability according to variety and origin classification, by integrating these 465 different behaviors of single analytical sources. 466 467 3.3. Data fusion models 468 With the goal of improving the classification results according to geographical 469 origin and grape variety, different strategies were assessed in the three data fusion 470 levels. Thus, in the case of having second-order data, several are the strategies that 471 could be adopted. 472 473 3.3.1. Low-level data fusion 474 PLS-DA was carried out in the first 1-DF option, directly on the concatenated 475 unfolded data matrix (Fig. 1). The validation results on the test samples are reported in 476 Table 1 and Table 2. 477 The models based on 1-DF achieved similar classification performances than 478 models from individual blocks when grape variety classification was evaluated. Despite 479 the two 1-DF options were able to correctly discriminate the same number of samples, 480 they did not improve the prediction results respect to NPLS-DA model from EEM data, 481 which obtained the best performance of all individual models. However, the option 1 482 reached better results in the calibration stage. 483 On the other side, the results obtained for geographical origin classification 484 showed relevant improvements of both 1-DF approaches in comparison with the 485 20 individual models, inasmuch as a total of 39 samples pf the training set were correctly 486 predicted. In this case, this strategy seemed to provide significantly better classification 487 results reaching 94.4% and 87.5% for NER and PREC, respectively. It is important to 488 highlight than these results exhibited an increment of more than 5% for NER and a great 489 improvement in PREC of more than 16%, displaying the sterling model ability to avoid 490 wrong predictions in the classes. 491 As a second option, a PCA can be also applied as a necessary step to compress 492 the information when algorithms as LDA are applied. Thus, it is important to be careful 493 inasmuch as, as in this case, the concatenated data from 1-DF consists on an extremely 494 large matrix where the number of irrelevant variables becomes larger than the really 495 meaningful ones and therefore, the selection of the more relevant variables could result 496 difficult [2, 40-41]. 497 The scores plot of the best 1-DF models for grape variety and geographical 498 origin classifications are shown in Fig. 3A and 3C, respectively. By comparing these 499 models to those for PLS-DA, obtained for the individual data matrices (Fig. II and III 500 SM), the improvement in the separation of classes by the DF models is clearer. 501 502 Insert here Fig. 3 503 504 Data fusion showing better discrimination ability than individual spectroscopies 505 have been also reported for fist-order data [36]. Indeed, most of the researches founded 506 in the literature carried out 1-DF on first-order data [10, 37–39] due to the ease of 507 performance together with the satisfactory results. Basically, 1-DF involves the 508 straightforward concatenation by combining variables of the data blocks. Thus, direct 509 first-order data concatenation is easier than second order-data concatenation since, in 510 21 these last, a prior step, e.g. data unfolding, could be needed when data arrays differ in 511 structure and complexity. In this case, fewer studies could be found in the literature 512 [18]. 513 514 3.3.2. Mid-level data fusion 515 As described above, two different approaches for 2-DF were evaluated. Option 1 516 was based on a first extraction of the relevant features by the development of a PCA 517 model for each unfolded data block, and then, the fusion of the PCA-scores matrices 518 obtained, being this matrix used in the development of the PLS-DA classification 519 models. Within this option, autoscaling or none-preprocessing were tested. The option 2 520 was based on the feature extraction by PARAFAC and Tucker3 of the EEM and CE- 521 DAD matrices, respectively, and then the fusion of the scores associated to the 3- 522 PARAFAC factors from EEM array and the 18-Tucker3 scores from CE-DAD array, 523 being the matrix used for building the PLS-DA classification models. 524 On the one hand, with regards to the two 2-DF options, by observing both grape 525 variety (Table 1) and geographical origin (Table 2) classification results for calibration 526 steps, the option 2 showed better classification results, calibrating correctly almost the 527 total of samples of the training set. On the other hand, by assessing the prediction rate of 528 grape variety classification (Table 1), it was again difficult to select the best option due 529 to once again, the two options were able to discriminate correctly the same amount of 530 samples for prediction set, but none of them was able to improve the performance 531 respect to the individual models. 532 Otherwise, the geographical origin classification rate of the option 2 was better 533 than the option 1 achieving 91.7 and 95.5 for NER and 79.2 and 87.5 for PREC, 534 22 respectively (Table 2). These results can be also observable by looking the scores plots 535 obtained by these PLS-DA models (bottom of Fig. 3B and Fig. 3D). 536 By making a general comparison of these 2-DF results with the individual 537 classification models, they also showed relevant improvements in the prediction rates in 538 comparison to the individual classification results (mainly for geographical origin 539 classification). However, similar classification results were achieved in comparison with 540 the 1-DF approaches, for both grape variety and geographical origin classification. 541 Nevertheless, better results in classification have been reported when 2-DF approach 542 was compared with the analysis of individual datasets or with 1-DF [14, 18, 22, 25, 42]. 543 Despite both low- and midlevels improved the individual classification results, 544 being similar between them, there are different advantages and disadvantages that could 545 be considered. For both cases, the data block obtained is then processed by the desired 546 chemometric technique. However, on the one hand, 1-DF only implies that the matrices 547 describing the individual blocks, after proper preprocessing, are concatenated to build a 548 single array, being easier even more if the data has a first-order structure. However, a 549 disadvantage of 1-DF is that typically data sets are obtained in which the number of 550 observations is much smaller than the number of variables, which prevents to apply 551 many multivariate data analysis techniques that are not directly applicable. The most 552 popular way of trying to solve the problem of many variables is to reduce the 553 dimensionality of each data matrix separately, before attempting to link them by means 554 of DF and this is how 2-DF works. 555 Otherwise, there are multiple possibilities that can be applied to carry out a 2-DF 556 strategy. The most remarkable techniques reported in the bibliography for multiway 557 data sets have been sequential and orthogonalized partial least squares (SO-PLS) [44] 558 and coupled matrix and tensor factorization (CMTF) [45]. Other approaches based on 559 23 multiblock analysis less used but also suitable in data fusion context, is the Common 560 Components and Specific Weights Analysis (CCSWA, also so-called ComDim) [18, 561 46]. 562 563 3.3.3. High-level data fusion 564 In this level of DF, two different approaches were also developed and assessed: 565 Majority Voting and Bayesian consensus methods. These approaches were implemented 566 by using the classification results of the 3 individual models (NPLS-DA, and PLS-DA 567 from the unfolded matrix and the extracted features matrix) of both analytical methods. 568 The classification results obtained by both approaches are shown in Table 1 and Table 569 2 for grape variety and geographical origin classification, respectively. 570 Concerning the prediction results of Bayesian consensus DF, the model 571 performed using the outputs of the individual NPLS-DA models for grape variety 572 classification provided the best results. Although this model could only match the 573 amount of samples correctly classified in the prediction set with the NPLS-DA 574 individual model from EEM data (NER = 81.1), it was able to improve the calibration 575 stage getting over in more than 15% in both indices NER and PREC. 576 Otherwise, for geographical origin classification, the Bayesian consensus model 577 developed from the PLS-DA results obtained with PARAFAC and Tucker3 scores 578 provided the best predictions. These results agreed with the classification results 579 obtained by the individual classification models discussed in section 3.2.2 and 3.2.3. 580 Therefore, in general terms, discrimination performances based on Bayesian high-level 581 fusion approaches resulted to be better than those obtained on single analytical sources, 582 as occurs in another work founded in the literature [25]. Hence, this improvement was 583 better observable in the case of geographical origin classification, for which the 584 24 Bayesian consensus fusion obtained the best prediction results achieving 97.2% and 585 91.7% for NER and PREC. This improvement could indicate that the reliability and 586 confidence of the final outcome are increased by the integration of heterogeneous 587 predictions. Moreover, classification performances have been previously reported by 588 means of Bayesian consensus 3- DF fusion achieving slightly better than those obtained 589 in the midlevel approach [25]. 590 However, the classification results obtained by the Majority Voting approach 591 were worse than the results obtained by the PLS-DA models made with the individual 592 data blocks. The main reason of that could be the fact that, considering only two 593 analytical techniques, the criteria applied was the “strict”, which means that only the 594 samples that were perfectly classified in both techniques could be classified into a 595 specific class. Hence, in the present study, there were many cases in which one 596 technique classified a sample to one class and the other technique classified the same 597 sample as another class, making that the final decision was “not-classified”. For this 598 reason, Majority Voting as 3-DF strategy should be preferably applied when three or 599 more techniques are studied simultaneously. 600 In comparison to the other two DF strategies (i.e. 1-DF and 2-DF), 3-DF has not 601 the problem of needing to adjust an adequate scaling due to each model is fitted 602 independently with its best scaling. However, a disadvantage of 3-DF is that the order 603 of combining the obtained predictions affects the final decisions. 604 As a final remark, it is important to highlight the evident improvement of the 605 classification results as level of data fusion increases. In fact, the improvement of the 606 DF prediction models can be linked in the level advance. Despite the combination of 607 multiple analytical sources increases the complexity of data treatment, this is 608 compensated by significantly better classification ability. 609 31 Methods to Classify Multiple Analytical Chemical Data, Data Handl. Sci. Techn. 752 31 (2019) 129-155. 753 [35] A. Fernández, A. Lombardo, R. Rallo, A. Roncaglioni, F. Giralt, E. Benfenati, 754 Quantitative Consensus of Bioaccumulation Models for Integrated Testing 755 Strategies, Environ. Int. 45 (2012) 51–58. 756 [36] A. Dankowska, W. Kowalewski, Tea Types Classification with Data Fusion of 757 UV–Vis, Synchronous Fluorescence and NIR Spectroscopies and Chemometric 758 Analysis, Spectrochim. Acta - Part A Mol. Biomol. Spectrosc. 211 (2019) 195– 759 202. 760 [37] B.P. Geurts, J. Engel, B. Ra, L. Blanchet, A. Suppers, E. Szyma, J.J. Jansen, 761 L.M.C. Buydens, Improving High-Dimensional Data Fusion by Exploiting the 762 Multivariate Advantage, Chemometr. Intell. Lab. 156 (2016) 231–240. 763 [38] Z. Haddi, H. Alami, N. El Bari, M. Tounsi, H. Barhoumi, A. Maaref, N. Jaffrezic- 764 renault, B. Bouchikhi, Electronic Nose and Tongue Combination for Improved 765 Classification of Moroccan Virgin Olive Oil profiles, Food Res. Int. 54 (2013) 766 1488–1498. 767 [39] Q.Q. Wang, H.Y. Huang, Y.Z. Wang, Geographical Authentication of 768 Macrohyporia Cocos by a Data Fusion Method Combining Ultra-Fast Liquid 769 Chromatography and Fourier Transform Infrared Spectroscopy, Molecules 24 770 (2019) 1320-1338. 771 [40] A.K. Smilde, M.J. van der Werf; S. Bijlsma, B.J.C. van der Werff-van der Vat, 772 R.H. Jellema, Fusion of Mass Spectrometry-Based Metabolomics Data, Anal. 773 Chem. 77 (2005) 6729–6736. 774 32 [41] S. Roussel, J. Roger, P. Grenier, Authenticating White Grape Must Variety with 775 Classification Models Based on Aroma Sensors , FT-IR and UV Spectrometry, J. 776 Food Eng. 60 (2003) 407–419. 777 [42] M. Silvestri, L. Bertacchini, C. Durante, A. Marchetti, E. Salvatore, M. Cocchi, 778 Application of Data Fusion Techniques to Direct Geographical Traceability 779 Indicators, Anal. Chim. Acta 769 (2013) 1–9. 780 [43] M. Cocchi, Introduction: Ways and Means to Deal With Data From Multiple 781 Sources, Data Handl. Sci. Techn. 31 (2019) 1-26. 782 [44] A. Biancolillo, T. Næs, R. Bro, I. Måge, Extension of SO-PLS to multi-way 783 arrays: SO-N-PLS, Chemom. Intell. Lab. Syst. 164 (2017) 113-126. 784 [45] E. Acar, R. Bro, A.K. Smilde, Data Fusion in Metabolomics Using Coupled 785 Matrix and Tensor Factorizations, P. IEEE 103 (2015) 1602-1620. 786 [46] M. Hanafi, G. Mazerolles, E. Dufour, E.M. Qannari, Common components and 787 specific weight analysis and multiple co-inertia analysis applied to the coupling 788 of several measurement techniques, J. Chemometrics 20 (2006) 172–183. 789 790 791 792 793 794 795 796 797 798 33 Figure captions 799 800 Figure 1. Schematic representation of data analysis workflow 801 Figure 2. Typical landscapes of (A) EEM and (B) CE-DAD data for a wine sample 802 showing within each geographical origin –Mendoza (M), San Juan (SJ), Río Negro 803 (RN) and Salta (S)- each grape variety -Chardonay (CH) Sauvignon blanc (SB) and 804 Torrontés (T)- 805 Figure 3. Scores plots for the first three LVs exhibiting the best classification results 806 obtained from (A and C) 1-DF and (B and D) 2-DF models showing the differentiation 807 among wines from (A and B) grape variety and (C and D) geographical origin 808 classifications. 95% confidence ellipses for each class are plotted in 3D in each scores 809 plot. 810 811 812 813 814 815 816 817 818 819 820 821 822 823 34 Figure 1 824 825 826 827 828 829 830 831 35 Figure 2 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 36 Figure 3 847 848 849 850 851 852 853 854 855 37 Tables 856 Table 1. Classification results according to grape variety (Chardonnay -CH-, Sauvignon 857 blanc –SB-, and Torrontés -TO-) obtained in the calibration and prediction stage from 858 individual data blocks (EEM and CE-DAD) and fused data (EEM-CE-DAD) evaluating 859 1-DF, 2-DF and 3-DF. For each model it is displayed the number of samples correctly 860 classified, not error rate (NER) and average precision (PREC) for both calibration 861 (CAL) and prediction (PRED) sets of each evaluated model. 862 863 GRAPE VARIETY CLASSIFICATION DATA STRUCTURE Correct classified samples CAL/PRED NER (CAL) NER (PRED) PREC (CAL) PREC (PRED) CH 24/18 SB 24/15 TO 24/12 EEM Unfolded data 24/9 18/9 18//6 83.3 53.3 86.1 64.3 Three-way data 18/15 15/9 18/12 70.8 81.1 71.0 82.1 3-factors PARAFAC scores 15/15 15/9 12/6 58.3 64.4 61.9 70.8 CE-DAD Unfolded data 24/15 24/3 24/9 100.0 59.4 100.0 66.7 Three-way data 18/15 21/6 24/9 87.5 66.1 87.8 70.8 Tucker3 scores 24/12 24/6 24/9 100.0 60.6 100.0 66.7 EEM-CE-DAD LOWLEVEL Opt. 1 24/15 24/6 24/9 100.0 66.1 100.0 74.1 MIDLEVEL Opt. 1 24/12 18/9 24/6 91.7 58.9 93.3 69.0 Opt. 2 24/15 24/3 24/9 100.0 59.4 100.0 66.7 HIGHLEVEL Bayesian consensus 24/18 21/0 24/9 95.8 58.3 100.0 58.3 18/15 21/9 24/12 87.5 81.1 87.8 82.1 24/15 24/9 24/9 100.0 72.8 100.0 77.1 Majority voting 24/6 18/0 18/3 83.3 19.4 86.1 40.7 18/12 12/6 18/9 66.7 60.6 67.2 65.7 15/9 15/6 12/6 58.3 50.0 61.9 52.2 864 865 866 867 868 869 870 38 871 Table 2. Classification results according to geographical origin (Mendoza –M-, Río 872 Negro –RN- San Juan –SJ-, and Salta –S-) obtained in the calibration and prediction 873 stage from individual data blocks (EEM and CE-DAD) and fused data (EEM-CE-DAD) 874 evaluating 1-DF, 2-DF and 3-DF. For each model it is displayed the number of samples 875 correctly classified, not error rate (NER) and average precision (PREC) for both 876 calibration (CAL) and prediction (PRED) sets of each evaluated model. 877 878 GEOGRAPHICAL ORIGIN CLASSIFICATION DATA STRUCTURE Correct classified samples CAL/PRED NER (CAL) NER (PRED) PREC (CAL) PREC (PRED) M 45/27 RN 6/6 SJ 12/6 S 9/6 EEM Unfolded data 36/18 6/3 12/3 9/3 95.0 54.2 85.0 60.4 Three-way data 24/15 3/3 9/3 9/3 69.6 51.4 62.0 47.9 3-factors PARAFAC scores 36/15 6/6 3/6 3/6 59.6 88.9 63.3 70.8 CE-DAD Unfolded data 45/24 6/0 12/3 9/0 100.0 34.7 100.0 27.9 Three-way data 33/21 6/0 9/3 9/6 87.1 56.9 77.5 50.8 Tucker3 scores 33/18 6/3 9/6 6/0 78.8 54.2 66.7 51.7 EEM-CE-DAD LOWLEVEL Opt. 1 39/21 6/6 9/6 9/6 90.4 94.4 85.7 87.5 MIDLEVEL Opt. 1 33/18 6/6 6/6 6/6 72.5 91.7 65.5 79.2 Opt. 2 36/21 6/6 12/6 9/6 95.0 95.5 85.0 87.5 HIGHLEVEL Bayesian consensus 45/21 6/6 12/6 9/3 100.0 81.9 100.0 84.4 39/15 6/6 12/6 9/6 96.7 88.9 91.7 75.0 39/24 6/6 12/6 9/6 96.7 97.2 86.7 91.7 Majority voting 36/18 6/0 12/0 9/0 95.0 16.7 85.0 13.6 21/12 3/0 6/0 9/3 61.7 23.6 55.9 25.0 27/12 6/3 3/6 3/0 54.6 48.6 46.3 35.1 879 880 Highlights 1) Second-order data were fused and chemometrically processed. 2) Multiple strategies for multi-levels data fusion were evaluated. 3) Straightforward approaches for classification purposes are presented. 4) Different degrees of improvement were observed on the results. 5) High-level strategy provided the best classification results. Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: